He has to implicitly (whether or not he includes the latest update to that other unvalidated partition) when he builds his block at the end of the chain that includes that other unvalidated partition. Longest chain wins so he won't want to ignore that last block.
By building on top of another partition's block, he increases the risk that his block will be orphaned because he has cannot tell if it contains a double spend. For him it is better not to build on the best block at all, but to maintain his own partitioned chain of blocks.
The partitions are strictly independent. Remember that.
Okay monsterer really. I must end this now. I am 100% certain my point is unarguable.
They are not independent when you combine them like that with the LCR rule. You must see that? Every block that partition A builds on top of partition B's block is essentially a merger of partitions A and B.
Sigh.
Independent partitions are not merged. The holistic Nash equilibrium (of the LCR) was explained.
monsterer can rescue his ego (and fill the thread with endless noise about his inability to connect the dots 3 pages ago) because many (most or all) readers are just as incapable as he is, so many will doubt what I wrote. Nevertheless my point was unarguable, but it isn't worth arguing to those are incapable.
monsterer can reply with some more nonsense. I am done arguing with him. Not because I lost, but because his ego desires a filibuster.
Make sure you are agreeing on the exact definition of a partition...
They aren't merged for the transactions nor for the Nash equilibrium of the blocks. There is no possible definition of strict(ly independent) partition for asset transfer that can support his position.